Mathematics

ECM1704 - Mathematical Investigations (2015)

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MODULE TITLEMathematical Investigations CREDIT VALUE15
MODULE CODEECM1704 MODULE CONVENERDr Barrie Cooper (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 weeks 0 0
Number of Students Taking Module (anticipated) 181
DESCRIPTION - summary of the module content

This module will introduce you to the process of mathematical research and help you to understand the nature of the mathematical research community that you will be joining at the University of Exeter.  An expert tutor will guide you through three short investigations as you develop a range of independent and group research skills across a variety of engaging topics.


The module will challenge and refine your concepts of knowledge and truth, as we explore the mathematical process in detail.  We will also carefully consider the ways in which mathematics can be communicated effectively, and you will have the opportunity to produce work in diverse media.


With an emphasis on teamwork and community building, this module also provides you with a great opportunity to meet your colleagues and lecturers on your mathematics degree programme. Furthermore, the module promises to be a rewarding introduction to your mathematical experience at the University of Exeter.

 

AIMS - intentions of the module

The module aims to give you an opportunity to: undertake open-ended investigations using mathematical material, and in doing so engage you in active learning; collaborate in small teams under the guidance of a member of staff and provide reinforcing material for other core stage one material in mathematics. In addition, it will provide you with an alternative to traditional lecture course teaching, and in doing so enrich your learning experience.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you should be able to:

 

Module Specific Skills and Knowledge:
1 work on your own or as part of a small team to formulate and solve both well defined and more open-ended problems in mathematics.
Discipline Specific Skills and Knowledge:
2 extract and formulate mathematical problems that are not explicitly stated, and to apply resultant solutions to the application;
3 present these solutions in a logical and coherent manner;
4 use mathematical computing software (such as MAPLE and MatLab) to assist problem solving.
Personal and Key Transferable/ Employment Skills and  Knowledge:
5 formulate and solve problems;
6 work effectively as part of a small team;
7 communicate orally with team members and via written presentation;
8 undertake research using a variety of sources;
9 identify the graduate employability skills developed during this module;
10 reflect critically on your experiences during the module.

SYLLABUS PLAN - summary of the structure and academic content of the module

Two topics for investigation will be chosen from a list that includes: 
 

- sequences and series;
- mathematical games;
- equivalence and order relations;
- matrices;
- number theory;
- random processes;
- graphs and networks;
- group theory.

However, any topic that supports (but is not essential to) the modules ECM1701, ECM1702 and ECM1408 would also be appropriate.

The remaining topic will study the nature of mathematics and scholarship at degree level.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 30.00 Guided Independent Study 120.00 Placement / Study Abroad 0.00
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning and teaching activities 30 1 hour lecture per week; 1 hour practical in a computer lab per week; 1 hour tutorial per week.
Guided independent study 120 Independent research for three 3-week investigations and associated assessments; development of LaTeX and other computing skills; preparation and revision for examination
     

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Progress updates 3 x 1 hour 1, 6, 7, 8, 9, 10 Peer and tutor
Draft submissions Once for each project (as project outputs) 1, 2, 3, 4, 5, 8 Peer and tutor
Skills self-assessment 1 hour 9 Peer feedback
Module surveys 3 x 30 minutes 10 Generic feedback
       

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 60 Written Exams 40 Practical Exams 0
DETAILS OF SUMMATIVE ASSESSMENT

Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Coursework – Group Project 1 20 5 - 10 minute video 1, 5, 6, 7, 8 Feedback sheet and peer feedback
Coursework – Group Project 2 20 3,000 words or equivalent 1, 2, 3, 4, 5, 6, 7, 8 Feedback sheet, annotated submission and peer feedback
Coursework - Group Project 3 20 3,000 words or equivalent 1, 2, 3, 4, 5, 6, 7, 8 Feedback sheet, annotated submission and peer feedback
Written Exam 40 2 hours 1, 2, 3, 5, 9, 10 Generic feedback
 
 

 

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-reassessment
All above Examination (100%) All August Ref/Def period
       
       

 

RE-ASSESSMENT NOTES

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.


If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

Basic reading:

Basic reading:

There is no particular set reading list for this module but students may be required to refer to the following

Houston, K  "How to think like a mathematician:  a companion to undergraduate mathematics" 1st, Cambridge University Press (2009), ISBN: 978-0521719780

ELE: http://vle.exeter.ac.uk

 

Web based and Electronic Resources:

Ideas from Mathematics Education - An Introduction for Mathematicians, Lara Alcock & Adrian Simpson.  Published by The Higher Education Academy: MSOR Network (2009). Available for download from <a href="http://www.ltsn.gla.ac.uk/index.php?pid=257" target="_blank">http://www.ltsn.gla.ac.uk/index.php?pid=257</a> (correct at 06/07/12).                                                                                
          
MSOR Subject Benchmark.  Developed by the QAA (2007). Available to read or download from <a href=" http://www.qaa.ac.uk/Publications/InformationAndGuidance/Pages/Subject-benchmark-statement-Mathematics-statistics-and-operational-research.aspx" target="_blank"> http://www.qaa.ac.uk/Publications/InformationAndGuidance/Pages/Subject-benchmark-statement-Mathematics-statistics-and-operational-research.aspx</a> (correct at 06/07/12).

 

Other Resources:

 

Reading list for this module:

There are currently no reading list entries found for this module.

CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES None
CO-REQUISITE MODULES None
NQF LEVEL (FHEQ) 4 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Friday 09 January 2015 LAST REVISION DATE Monday 12 January 2015
KEY WORDS SEARCH Mathematical research